Externalist theories of representation (including most naturalistic psychosemantic theories) typically require some relation to obtain between a representation and what it represents. As a result, empty concepts cause problems for such theories. I offer a naturalistic and externalist account of empty concepts that shows how they can be shared across individuals. On this account, the brain is a general-purpose model-building machine, where items in the world serve as templates for model construction. Shareable empty concepts arise when there is a common template for different individuals' concepts, but where this template is not what the concept denotes